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Leonhard Euler (1707–1783) was born in Basel, Switzerland. Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. When its variable is the number pi, Euler's formula evaluates to Euler's identity. On the other hand, the Yang–Baxter equation is considered the most beautiful equation by many scholars. In this book, we study connections between Euler’s formulas and the Yang–Baxter equation. Other interesting sections include: non-associative algebras with metagroup relations; branching functions for admissible representations of affine Lie Algebras; super-Virasoro algebras; dual numbers; UJLA structures; etc.

transcendental numbers --- Euler formula --- Yang–Baxter equation --- Jordan algebras --- Lie algebras --- associative algebras --- coalgebras --- Euler’s formula --- hyperbolic functions --- UJLA structures --- (co)derivation --- dual numbers --- operational methods --- umbral image techniques --- nonassociative algebra --- cohomology --- extension --- metagroup --- branching functions --- admissible representations --- characters --- affine Lie algebras --- super-Virasoro algebras --- nonassociative --- product --- smashed --- twisted wreath --- algebra --- separable --- ideal --- n/a --- Yang-Baxter equation --- Euler's formula